To provide for continuous compensation for unbalance of a rotary member such as a grinding wheel, for example during on-going operation thereof, it is possible to provide an arrangement comprising an annular container which is coaxially fixed to the rotary member to be balanced. The annular container is subdivided in its circumferential direction into a plurality of balancing chambers at different angular positions, into which a compensating medium such as a fluid can be selectively introduced from the exterior of the annular container, to provide for compensation in respect of unbalance of the rotary member. However, in operation of such an arrangement on a rotary member such as a balancing wheel, more an more compensating fluid is introduced into the balancing chambers for each respective unbalance compensating operation which has to be carried out, so that the balancing chambers become progressively filled to such an extent that it is ultimately no longer possible to provide an unbalance compensating effect. In that case the balancing chambers have to be emptied again. Provided for that purpose are chamber emptying valves which are operatively associated with the respective balancing chambers. The chamber emptying valves are actuated by an actuating member in the form of an annular deflector plate which acts on and thus actuates the respective chamber emptying valves by way of spring-loaded, axially disposed valve displacement elements which are in the form of push rod members. The deflector plate is actuated by nozzles which are disposed in directly opposite relationship to the plate, in an annular duct, and through which a pressure fluid can be directed on to the plate. In order to produce simultaneous displacement of the plate over the entire circumference thereof, that arrangement requires a comparatively large number of nozzles for directing pressure fluid on to the plate around the circumferential extent thereof. In addition, to provide for transmission of the control movement of the plate to the valve members of the chamber emptying valves, besides the spring-loaded, axially displaceable push rod members acting as valve displacement members to operate the chamber emptying valves, that arrangement also has single-arm levers which are associated with respective ones of the chamber emptying valves and which are actuated by virtue of the axial movement of the push rod members. When the levers are pivoted, they displace the respective valve members of the chamber emptying valves which are in the form of non-return or check valves. Therefore, to provide for the simultaneous opening of all the chamber emptying valves, the assembly requires a relatively large number of individual components which means that the amount of work involved in final assembly of the system is high.